Organising the toolbox in statistics and operations research

Don’t bury students in tools

In our statistics courses and textbooks there is a tendency to hand our students tool after tool, wanting to teach them all they need to know. However students can feel buried under these tools and unable to decide which to use for which task. This is also true in beginning Operations Research or Management Science courses. To the instructors, it is obvious whether to use the test for paired or independent samples or whether to use multicriteria decision making or a decision tree. But it is just another source of confusion for the student, who wants to be told what to do.

Tools for statistics and operations research

A common approach to teaching hypothesis testing in business statistics courses, if textbooks are anything to go by, is to teach several different forms of hypothesis testing, starting with the test for a mean, and test for a proportion then difference of two means, independent and paired, then difference of two proportions. Then we have tests for regression and correlation, and chi-squared test for independence. These are the seven basic statistical tests that people are likely to use or see. I would probably add ANOVA, if there is enough time. Even listed, this seems a bit confusing.

An introductory operations research course might include any number of topics including linear programming, integer programming, inventory control, queueing, simulation, decision analysis, critical path, the assignment problem, dynamic programming, systems analysis, financial modelling, inventory control…And I would hope some overall teaching about models and the OR process.

Issues with the pile of tools

Of course we need to teach the essential tools of our discipline, but there are two issues arising from this approach.

The obvious one is that students are left bewildered as to which test they should use when. Because of the way textbooks and courses are organised, students don’t usually have to decide which tool to use in a given situation. If the preceding chapter is about linear programming, then the questions will be about linear programming.

The second issue is that unless students are helped, they fail to see the connections between the techniques and are left with a fragmented view of the discipline. It is not just a question of which tool to use for which task, it is about seeing the linkages and the similarities. We want to help them have integrated knowledge.

Providing activities to help with organisation

In both my introductory courses I attempted to address this, with varying degrees of success.

In our management science course we end the year with a case of a situation with multiple needs, and the students were to identify which technique would be useful in each instance. Then the final exam has a similar question, with specific questions about over-arching concepts such as deterministic and stochastic inputs, and the purpose of the model – to optimise or inform. This is also an opportunity to address issues of ethics and worldview.

In the final section of the business statistics course we have a large bank of questions for students to work through, to give them practice in deciding which test to use. I was careful to make sure that there was more than one question related to each scenario, so that students would not learn unhelpful shortcuts, such as, if the question is about weight loss, the answer must be paired difference of two means. I also analysed the mistakes given in multichoice answers, to see where confusion was arising, sometimes due to poor wording. From this I refined the questions.

Examples of the questions for test choice in hypothesis testing

Management thinks there is a difference in productivity between the two days of the week in a certain work area. The production output of a random sample of 15 factory workers is recorded on both a Tuesday and a Friday of the same week. For each worker, the number of completed garments is counted on both days.

A restaurant manager is thinking of doing a special “girls’ night out” promotion. She suspects that groups of women together are more likely to stay for dessert than mixed adult or family groups. For the next two weeks she gets the staff to write down for each table whether they stay for dessert, and what type of group they are. She asks you to see if her suspicion is correct.

A human resources department has data on 200 past employees, including how long, in months, they stayed at the company, and the mark out of 100 they got in their recruitment assessment. They ask you to work out whether you can predict how long a person will stay, based on their test mark.

A researcher wanted to investigate whether a new diet was effective in helping with weight loss. She got 40 volunteers and got 20 to use the diet and the other 20 to eat normally. After 6 weeks the weights (in kg) before and after were recorded for each volunteer, and the difference calculated. She then looked at how the weight losses differed between the two groups.

Comment on the questions

You might notice that all the examples are in a business context. This is because this is a course for business students, and they need to know that what they are learning is relevant to their future. Questions about dolphins and pine trees are not suitable for these students. (Unless we are making money out of them!)

The master diagram

The students to work through these multiple choice questions on-line, and we offered help and coached them through questions with which they had difficulty. By taking my turn with the teaching assistants in the computer labs, I was able to understand better how the students perceived the tests, and ways to help them with this. The result is a diagram, or set of diagrams which shows the relationships between the tests, and a procedure to help them make the decision. I am a great believer in diagrams, but they need to be well thought out. Many textbooks have branching diagrams, showing a decision process for which test to use. I felt there was a more holistic way to approach it, and thought long and hard, and tried out my diagrams on students before I came up with our different approach. You can see the diagrams here by clicking on the link to the pdf which you can download: Choosing the test diagrams

The three questions which help the students to identify the most appropriate test are:

What level of measurement is the data – Nominal or interval/ratio?

How many samples do we have?

What is the purpose of our analysis?

I made an on-line lesson which takes the students through the steps over and over, and created the diagrams to help them. Time and again the students said how much it helped them to fit it all together. Eventually I made the following video, which is on YouTube. I suspect it must be coming up to summary time in courses in the US, as this video has recently attracted a lot of views, and positive comments.
The video is also part of our app, AtMyPace: Statistics along with two sets of questions to help students to learn about the different types of tests and how to tell them apart. You can access the same resources on-line through AtMyPace:Statistics statsLC.com.

It is important to see the subject as a whole, and not a jumbled mass of techniques and ideas, and this has really helped my students and many others through the video and app.

Best wishes for the holiday season

It is Christmas time and here in Christchurch the sun is shining and barbecues and beaches are calling. I am taking a break from the blog for the great New Zealand shut-down and will be back in the New Year.

Thank you for all the followers and especially your comments, Likes and ReTweets.